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Guidance

In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. A rotation is an example of a transformation where a figure is rotated about a specific point (called the center of rotation), a certain number of degrees.

For now, in order to graph a rotation in general you will use geometry software. This will allow you to rotate any figure any number of degrees about any point. There are a few common rotations that are good to know how to do without geometry software, shown in the table below.

Center of Rotation

Angle of Rotation

Preimage (Point
)

Rotated Image (Point
)

(0, 0)

(or
)

(0, 0)

(or
)

(0, 0)

(or
)

Example A

Line
drawn from (-4, 2) to (3, 2) has been rotated about the origin at an angle of
CW. Draw the preimage and image and properly label each.

Solution:

Example B

The diamond
is rotated
CCW about the origin to form the image
. On the diagram, draw and label the rotated image.

Solution:

Notice the direction is counter-clockwise.

Example C

The following figure is rotated about the origin
CW to make a rotated image. On the diagram, draw and label the image.

Solution:

Notice the direction of the rotation is counter-clockwise, therefore the angle of rotation is
.

Concept Problem Revisited

Quadrilateral
has coordinates
and
. Draw the quadrilateral on the Cartesian plane. Rotate the image
counterclockwise about the point
. Show the resulting image.

Vocabulary

Center of rotation

A
center of rotation
is the fixed point that a figure rotates about when undergoing a rotation.

Rotation

A
rotation
is a transformation that rotates (turns) an image a certain amount about a certain point.

Image

In a transformation, the final figure is called the
image
.

Preimage

In a transformation, the original figure is called the
preimage.

Transformation

A
transformation
is an operation that is performed on a shape that moves or changes it in some way. There are four types of transformations: translations, reflections, dilations and rotations.

Guided Practice

1. Line
drawn from (-3, 4) to (-3, 8) has been rotated
CW about the point
. Draw the preimage and image and properly label each.

2. The polygon below has been rotated
CCW about the origin. Draw the rotated image and properly label each.

3. The purple pentagon is rotated about the point
. Find the coordinates of the purple pentagon. On the diagram, draw and label the rotated pentagon.

Answers:

1.

Notice the direction of the angle is clockwise, therefore the angle measure is
CW or
.

2.

Notice the direction of the angle is counter-clockwise, therefore the angle measure is
CCW or
.

3.

The measure of
. Therefore
or
. Notice the direction of the angle is counter-clockwise, therefore the angle measure is
CCW or
.

Explore More

Rotate the above figure
clockwise about the origin.

Rotate the above figure
clockwise about the origin.

Rotate the above figure
about the origin.

Rotate the above figure
counterclockwise about the origin.

Rotate the above figure
counterclockwise about the origin.

Rotate the above figure
about the origin.

Rotate the above figure
clockwise about the origin.

Rotate the above figure
clockwise about the origin.

Rotate the above figure
about the origin.

Rotate the above figure
counterclockwise about the origin.

Rotate the above figure
counterclockwise about the origin.

Rotate the above figure
about the origin.

Rotate the above figure
clockwise about the origin.

Rotate the above figure
clockwise about the origin.

Rotate the above figure
about the origin.

Rotate the above figure
counterclockwise about the origin.

Rotate the above figure
counterclockwise about the origin.

Rotate the above figure
about the origin.

Rotate the above figure
clockwise about the origin.

Rotate the above figure
clockwise about the origin.

Rotate the above figure
about the origin.

Rotate the above figure
counterclockwise about the origin.

Rotate the above figure
counterclockwise about the origin.

Rotate the above figure
about the origin.

Image Attributions

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Description

This concept explores graphing a rotation given a description of the rotation.